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General Vector Spaces

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that if V and W are three dimensional subspaces of R5, then V and W must have a nonzero vector in common.


    2. Relevant equations
    NA


    3. The attempt at a solution
    I've attempted to set up the problem by writing out,

    V = { (1, 0, 0, 0, 0), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0) }
    W = { (0, 0, 0, 1, 0), (0, 0, 0, 0, 1), (1, 1, 0, 0, 0) }

    After that, I'm lost.

    I don't really like vector spaces because I don't understand it very well. So could whoever explain please explain thoroughly? =P I would help a lot because I want to know what's going on! hehe, thanks in advance =)
     
  2. jcsd
  3. Nov 2, 2009 #2

    lanedance

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    Homework Helper

    rather than narrowing in on a single case, think aobut linear independence... what is the maximal number of linearly independent vectors, in any subspace of R^3?

    similarly, how many vectors are in a the basis for R^5?
     
    Last edited: Nov 2, 2009
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